Unexpected Roles of Guest Polarizability and Maximum Hardness

J. Am. Chem. Soc. 1996, 118, 10257-10268

10257

Unexpected Roles of Guest Polarizability and Maximum Hardness, and of Host Solvation in Supramolecular Inclusion Complexes: A Dual Theoretical and Experimental Study Rene´ Castro, Marcelo J. Berardi, Emilio Co´ rdova, Mariluz Ochoa de Olza, Angel E. Kaifer, and Jeffrey D. Evanseck* Contribution from the Department of Chemistry, UniVersity of Miami, 1301 Memorial DriVe, Coral Gables, Florida 33146-0431 ReceiVed March 4, 1996. ReVised Manuscript ReceiVed July 29, 1996X

Abstract: The origin of differential binding affinity and structural recognition between the inclusion complexes of cyclobis(paraquat-p-phenylene), 14+, and 1,4-substituted phenyl or 4,4′-substituted biphenyl derivatives has been jointly determined by spectrometric techniques and ab initio and semiempirical molecular orbital methods. The unusual boxed geometry and tetracationic charge distribution in 14+ are key molecular features which produce strong intermolecular interactions with guest and solvent molecules. Solvation was addressed by including up to 12 acetonitrile molecules in the theoretical model, which realigned the predicted gas-phase supramolecular structures and energies into excellent agreement with experiment. The computed complexation enthalpies, ∆Hbind, from the semiempirical molecular orbital PM3 method are on average within 1 kcal/mol of the experimental free energy binding data collected from absorption spectroscopy in acetonitrile. In addition, the computed geometric penetration and positioning of 14+/benzidine and 14+/4,4′-biphenol complexes are consistent with that reported from NMR NOE data. The partitioning of self-consistent field complexation energies from both classical and quantum forces has been determined by using Morokuma’s variational energy decomposition technique. It was determined that the primary basis for the molecular recognition between 1,4-substituted phenyl guests and 14+ is short-range stabilizing electrostatic forces complemented by small amounts of polarizability and charge-transfer. In contrast, the recognition force between 4,4′-substituted biphenyl guests and 14+ is dominated by polarizability with a small contribution from electrostatics. Therefore, the balance between molecular polarizability and electrostatics controls the differential binding affinity and structural recognition with 14+. For the first time, we report that individual molecular properties of substituted guests correlate with the binding energies of corresponding 14+ inclusion complexes. Direct correlations between the 14+ binding energies and the computed molecular polarizability, maximum hardness, softness, and electronegativity of the guest have been identified. It is now plausible to consider the design and construction of new supramolecular assemblies based upon a few select molecular properties of the constituent molecules.

Introduction Recent advances in supramolecular chemistry have had a major impact on the understanding of structural and reactive aspects of biological chemistry and the design and manipulation of new materials.1 The single concept common throughout supramolecular chemistry revolves around the study of molecular association. More specifically, the clear depiction of the structural, energetic, and dynamic character of the intermolecular bond can provide insight into the fundamental forces required for the rational design of nanoscale molecular devices and the spontaneous assembly of supramolecular systems. Our interest in understanding intermolecular binding forces derives from the recent work with the tetracationic cyclophane receptor cyclobis(paraquat-p-phenylene), 14+.2-6 The 14+ receptor has gained substantial prominence as a versatile molecular host and as a fundamental component of a large number of catenanes and rotaxanes.3 As a receptor, 14+ shows considerable affinity for molecules containing electron-rich aromatic rings. It has been shown3a that 14+ forms stable inclusion complexes Abstract published in AdVance ACS Abstracts, September 15, 1996. (1) (a) Lehn, J.-M. Supramolecular Chemistry Concepts and PrespectiVes; VCH: Deerfield Beach, FL, 1995. (b) Amabilino, D. B.; Stoddart, J. F. Chem. ReV. 1995, 95, 2725. (c) Philp, D.; Stoddart, J. F. Angew. Chem., Int. Ed. Engl. 1996, 35, 1154. (2) Odell, B.; Reddington, M. V.; Slawin, A. M. Z.; Spencer, N.; Stoddart, J. F.; Williams, D. J. Angew. Chem., Int. Ed. Engl. 1988, 27, 1547. X

S0002-7863(96)00700-7 CCC: $12.00

with a variety of π-donors, in which the aromatic ring of the donor guest penetrates the cavity of the host, establishing a balance of favorable and repulsive interactions between the host’s electron deficient bipyridinium (paraquat) groups and the electron-rich ring(s) of the guest. In spite of the numerous (3) (a) Anelli, P. L.; Ashton, P. R.; Ballardini, R.; Balzani, V.; Delgado, M.; Gandolfi, M. T.; Goodnow, T. T.; Kaifer, A. E.; Philp, D.; Pietraszkiewicz, M.; Prodi, I.; Reddington, M. V.; Slawin, A. M. Z.; Spencer, N.; Stoddart, J. F.; Vicent, C.; Williams, D. J. J. Am. Chem. Soc. 1992, 114, 193. (b) Amabilino, D. B.; Ashton, P. R.; Reder, A. S.; Spencer, N.; Stoddart, J. F. Angew. Chem., Int. Ed. Engl. 1994, 33, 1286. (c) Amabilino, D. B.; Ashton, P. R.; Brown, C. L.; Co´rdova, E.; Godıńez, L. A.; Goodnow, T. T.; Kaifer, A. E.; Newton, P.; Pietraszkiewicz, M.; Philp, D.; Raymo, F. M.; Reder, A. S.; Rutland, M. T.; Slawin, A. M. Z.; Spencer, N.; Stoddart, J. F.; Williams, D. J. J. Am. Chem. Soc. 1995, 117, 1271. (d) Co´rdova, E.; Bissell, R. A.; Kaifer, A. E. J. Org. Chem. 1995, 60, 1033. (e) Benniston, A. C.; Harriman, A.; Lynch, V. M. J. Am. Chem. Soc. 1995, 117, 5275. (4) Benniston, A. C.; Harriman, A.; Philp, D.; Stoddart, J. F. J. Am. Chem. Soc. 1993, 117, 5298. (5) Co´rdova, E.; Bissell, R. A.; Spencer, N.; Ashton, P. R.; Stoddart, J. F.; Kaifer, A. E. J. Org. Chem. 1993, 58, 6550.

© 1996 American Chemical Society

10258 J. Am. Chem. Soc., Vol. 118, No. 42, 1996 investigations in which host 14+ has played a crucial role, the significant aspects of its selectivity and binding properties determined by intermolecular association are still poorly understood. For instance, charge-transfer interactions were originally thought to dominate the overall stability of 14+ inclusion complexes, but recently have been determined to have a rather diminished role since p-phenylenediamine (PDA)4 and benzidine (BZ)3d,5 are two π-donor guests for which the order of π-donating ability (PDA > BZ) is opposite that of the stability of the corresponding inclusion complexes with 14+ (BZ > PDA). Given the importance of host 14+ in the design and synthesis of electrochemically and chemically switchable rotaxanes,6 photoactive rotaxanes,3e and other molecular devices,7 it is both appropriate and timely to address the primary intermolecular factors which determine the stability of its inclusion complexes. It is our intention to evaluate the composition of intermolecular bonding which governs the overall strength and structure found in these particular supramolecular systems. We employed ab initio molecular orbital theory along with variational energy decomposition techniques to quantify the noncovalent forces prevalent in the inclusion complexes of 14+. The long-term goal of this work is to provide a refined and more rational methodology to design new high-performance molecular devices. Computational and Experimental Procedure All calculations were performed using the SPARTAN 4.0/4.1,8 GAUSSIAN 92/94,9,10 and MONSTERGAUSS11 software packages on an IBM RS/6000 Model 590 workstation equipped with 512 Mbyte of physical memory and 9 Gbyte of disk space. Geometry optimizations were carried out using restricted Hartree-Fock theory with the STO3G, 3-21G, 6-31G(D), and 6-31G(P,D) basis sets for ab initio calculations,12 or with the MNDO, AM1, or PM3 semiempirical method.13-15 No assumptions were made concerning the symmetry of the complexes, unless stated otherwise. Frequency calculations demonstrate that each complex is a true minimum on the potential energy surface. The details of each calculation are provided in the supporting information. We have conducted UV-vis binding studies and compiled a comprehensive list of binding energies and charge-transfer band λmax values for a variety of substituted phenyl and biphenyl compounds. UV-vis binding studies were conducted on a Shimadzu UV-2101PC computer-controlled scanning spectrophotometer with a temperature control module. In a typical experiment, a 0.8 mM cyclophane solution (6) Bissell, R. A.; Co´rdova, E.; Kaifer, A. E.; Stoddart, J. F. Nature 1994, 369, 133. (7) The accessible redox chemistry of host 14+ has been utilized to design voltammetric molecular sensors. See, for instance: (a) Bernardo, A. R.; Stoddart, J. F.; Kaifer, A. E. J. Am. Chem. Soc. 1992, 114, 10624. (b) Rojas, M. T.; Kaifer, A. E. J. Am. Chem. Soc. 1995, 117, 5883. (8) SPARTAN 4.0 and 4.1, Wavefunction, Inc., Irvine, CA. (9) GAUSSIAN 92/DFT, Revision G.4, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. W. Wong, J. B. Foresman, M. A. Robb, M. Head-Gordon, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 1993. (10) GAUSSIAN 94, Revision B.3, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. AlLaham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsburgh, PA, 1995. (11) MONSTERGAUSS, Peterson, M., University of Toronto; Poirier, R., Memorial University of Newfoundland, 1991. (12) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986. (13) Dewar, M. J. S.; Thiel, W. J. Am. Chem. Soc. 1977, 99, 4899. (14) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (15) Stewart, J. J. P. J. Comput. Chem. 1989, 209, 221.

Castro et al.

Figure 1. Distances (Å) and angles (degrees) of 14+ given by PM3, AM1, RHF/6-31G(D), and X-ray crystallography. in dry CH3CN was titrated with a 200 mM stock solution of the guest also containing 0.8 mM cyclophane to maintain a constant cyclophane concentration. Some guests were run at lower concentrations due to solubility limitations. Absorption readings were taken at λmax for the charge-transfer band of the complex, and the absorption was corrected for any overlapping absorption of the guest in that region by blank subtraction when necessary. The data were fit to a binding isotherm equation using a least squares algorithm as described elsewhere.3d

Results and Discussion Cyclobis(paraquat-p-phenylene). We have computed the gas-phase structure of 14+ at several levels of theory and have made a detailed comparison with the X-ray crystal structure, as shown in Figure 1. The crystal structure of 1(PF6)4(MeCN)3 has been previously reported.2 The solid state structure is most likely a good representation of 14+ in the condensed liquid and gas phases since its cyclic constraints render an inflexible molecular framework with severely limited conformational freedom. Our first goal was to establish a level of theory which provided trustworthy structural information on the cyclophane as compared to X-ray crystallography. The strengths and weaknesses of semiempirical methods have been reported.16-22 The general conclusion derived from the existing literature is that it is necessary to critically examine the computational methods on model systems closely related to the chemistry of interest. Thus, we have compared MNDO, AM1, PM3, and ab initio methods against experimental structural data for 4,4′-substituted biphenyl systems.23 Gas(16) Smith, D. A.; Ulmer, C. W. II; Gilbert, M. J. J. Comput. Chem. 1992, 13, 640. (17) Verwoerd, W. S.; Weimer, K. J. Comput. Chem. 1991, 12, 417. (18) Martin, J. M. L.; Franç ois, J. P.; Gijbels, R. J. Comput. Chem. 1991, 12, 52. (19) Fabian, W. M. F. J. Comput. Chem. 1991, 12, 17. (20) Burke, L. A.; Krishnan, P. N.; Morris, R. E.; Famini, G. R. J. Phys. Org. Chem. 1992, 5, 614. (21) Holder, A. J.; Evleth, E. M. In Modeling the Hydrogen Bond; Smith, D. A., Ed.; ACS: Washington, DC, 1994. (22) Scano, P.; Thomson, C. J. Comput. Chem. 1991, 12, 172. (23) Ochoa de Olza, M.; Davey, C. A.; Evanseck, J. D. Manuscript in preparation.

Supramolecular Inclusion Complexes

J. Am. Chem. Soc., Vol. 118, No. 42, 1996 10259

Table 1. Computed Energies of Complexation between Monosubstituted Phenyl Guests and 14+ a system benzene

toluene phenol anisole aniline

tert-butylbenzene

thiophenol thioanisole

no. of MeCN molecules

type

Hguest

0 4 12 0 2 4 6 12 0 12 2 2 12 0 12 12 0 12 0 12 12 0 12 0 12 2 12 2 12

π π π σ σ σ σ σ σ σ σc σd σd σe σe σf σg σg σh σh avi π π σ σ σ σ σ σ

23.455

14.090 -21.672

-14.553

21.295

0.321

27.670 23.243

Hcomplex

∆Hbind

1092.101 1110.285 1174.158 1089.044 1096.768 1108.316 1115.437 1173.003 1078.063 1163.166 1047.282 1047.835 1126.533 1046.240 1132.798 1134.316 1082.587 1169.210 1082.587 1171.148 1170.179 1064.246 1149.033 1062.964 1148.400 1095.220 1176.451 1090.020 1170.972

-2.29 -1.39 -0.52 -5.35 -4.03 -3.35 -3.06 -1.67 -6.96 -2.14 -8.39 -7.84 -3.01 -10.14 -3.87 -2.35 -9.65 -3.30 -9.65 -1.37 -2.33 -7.01 -2.51 -8.29 -3.14 -9.80 -2.44 -10.57 -3.49

∆Gbind

K

λmax

-1.68

17b

290

1295

-1.64

16b

319

1675

-2.14

37

411

587

-1.74

19

410

600

-2.64

86

496

556

333

1040

445

656

-0.95

-1.71

5b

18

a

Binding is described as π type if it is truly an inclusion complex and as σ type if it is centered about but not completely inserted into the cyclophane. Energies are reported in kcal/mol, association constants in M-1, λmax in nm, and in M-1 cm-1. b Data from Benniston, A. C.; Harriman, A.; Philp, D.; Stoddart, J. F. J. Am. Chem. Soc. 1993, 117, 5298. c The OH substituent is oriented away from the 14+ cavity. d The OH substituent is oriented toward the 14+ cavity. e The OMe substituent is oriented toward the 14+ cavity. f The OMe substituent is oriented away from the 14+ cavity. g The NH2 substituent is oriented away from the 14+ cavity. h The NH2 substituent is oriented toward the 14+ cavity. i The averaged value of two conformations is compared with experiment.

phase electron diffraction experiments24 and high-level ab initio calculations25 show that the twisted biphenyl conformations (∼44°) are separated by coplanar and perpendicular transition structures. MNDO yields an incorrect potential energy surface, whereas AM1 and PM3 give qualitatively correct structures and energies.23 Our computational model for 14+ involves the D2 and C1 structures. Frequency analysis reveals that the computed structures from each point group are local minima (except MNDO). The important geometric features of 14+ are summarized in Figure 1. Upon close inspection, it is clear that both the AM1 and PM3 semiempirical and ab initio methods yield satisfactory agreement with the X-ray structure. The MNDOgenerated structure is strongly distorted and resulted in the least satisfactory agreement with experiment. The model was then redefined to include four chloride anions. The computations were carried out using AM1, PM3, MNDO, and RHF/STO-3G. The effect of the counterions improved some of the obvious structural deficiencies, but introduced more geometric and energetic error than the simple 14+ model. Therefore, to probe binding energies and geometries, along with the forces operating within the binding cavity, we reverted back to the gas-phase 14+ computational model with no counterions. The energy differences between the D2 and C1 symmetric forms of 14+ are less than 1 kcal/mol (excluding MNDO). This suggests that it is possible for 14+ to have a number of accessible conformational states which may contribute to the phenomenon of guest inclusion or in the dynamic transfer of 14+ along the thread of a rotaxane or molecular shuttle.6 Therefore, we (24) Almenningen, A.; Bastiansen, O.; Fernholt, L.; Cyvin, B. N.; Cyvin, S. J.; Samdal, S. J. Mol. Struct. 1985, 128, 59. (25) Rubio, M.; Merchań, M.; Ortı´, E. Theor. Chim. Acta 1995, 91, 17.

employed the method of “corner flapping” 26 to exhaustively explore the possibility of 14+ ring conformations using the PM3 semiempirical method. The corner flapping method exploits the reduced conformational space of cyclic structures which avoids some of the inherent problems of random and systematic search procedures. We defined the central bipyridinium and corner methylene bonds as rotatable. In all, 59 trial conformations were generated and only 1 true conformation was retained using the PM3 Hamiltonian. The resulting D2 structure is virtually identical with that of C1. Thus, the potential energy surface of 14+ is not complicated with many energy extrema. On the other hand, the energy cost to distort the bipyridinium and p-xylylene torsional angles is very small. The bipyridinium torsional angle can deviate 20° before destabilizing up to 1 kcal/ mol, which may contribute to the dynamic behavior of rotaxanes and molecular shuttles in solution.27 Aromatic Molecule-Cyclophane Inclusion Complexes. Three earlier computational studies specifically targeted the understanding of 14+ complexation with small aromatic guests.28-30 Ricketts et al. used the CFF91 force field to account for nonbonding interactions between 14+ and both simple and extended aromatic guest molecules.28 The dominant binding forces were reported to be the electrostatic interactions between (26) (a) Goto, H.; Osawa, E. J. Am. Chem. Soc. 1989, 111, 8950. (b) Goto, H.; Osawa, E.; Yamato, M. Tetrahedron 1993, 49, 387. (27) Kaifer, A. E.; Evanseck, J. D. Work in progress. (28) Ricketts, H. G.; Stoddart, J. F.; Hann, M. M. In Computational Approaches in Supramolecular Chemistry; Wipff, G., Ed.; Kluwer Academic Publishers: Boston, MA, 1994. (29) Smit, E. A.; Lilienthal, R. R.; Fonseca, R. J.; Smit, D. K. Anal. Chem. 1994, 66, 3013. (30) Odell, B.; Reddington, M. V.; Slawin, A. M. Z.; Spencer, N.; Stoddart, J. F.; Williams, D. J. Angew. Chem., Int. Ed. Engl. 1988, 27, 1547.

10260 J. Am. Chem. Soc., Vol. 118, No. 42, 1996

Castro et al.

Figure 2. Electrostatic potential plot (+250 kcal/mol) of 14+.

Figure 4. Comparison of RHF/STO-3G and PM3 complexes of 14+ and p-phenylenediamine.

Figure 3. Electrostatic potential plot (-5 kcal/mol) of benzidine.

the phenolic oxygen lone pairs of the π-rich guest molecule and electron deficient parts of the paraquat units. Smit et al.29 and Odell et al.30 have applied AM1 to 14+ complexes of xylene and dicyanobenzene, and found strong electrostatic forces which yielded structures consistent with those reported by X-ray crystallography. Smit et al. also predicted that enthalpy controls the binding of complexation and not the entropy, where enthalpy changes follow electronic donor-acceptor considerations.29 The inclusion complexes of 14+ studied within this investigation involve 1,4-substituted phenyl and 4,4′-substituted biphenyl derivatives. The guests of greatest interest are hydroquinone (2), p-phenylenediamine (3), 4,4′-biphenol (4), and benzidine (5), since they are fundamental units of the docking stations

used in recently reported rotaxanes3,5 and molecular shuttles.6 Over 20 substituted phenyl and biphenyl systems incorporating systematic electronic and structural changes have been examined with receptor 14+, as listed in Tables 1-4.

Figure 5. Three conformations and complexation energies of benzene and 14+ computed using PM3.



Table 2. Computed Energies of Complexation between Disubstituted Phenyl Guests and 14+ a system p-xylene 1,4-dichlorobenzene hydroquinone

1,4-dimethoxybenzene p-phenylenediamine

1,4-dimercaptobenzene p-chloroaniline (C2V) p-chlorophenol

p-nitroaniline p-fluorotoluene p-methoxytoluene


type

0 12 0 12 12 0 0 0 12 0 12 0 12 0 0 12 0 0 2 12 12 0 12 12 12 0 12 12 0 12 12 0 12 12

π π π π σ πc πd σ σ σ σ π π π σ σ σ σ σe σe avi σf σf σd avg σh σh avi σj σj avi σd σd avi

Hguest 4.740 10.112

-66.063

-51.899 19.489

32.001 18.626

-28.390

10.685

-29.612

-23.816

Hcomplex

∆Hbind

1073.015 1154.457 1080.326 1161.754 1159.599 1004.611 999.509 998.086 1082.696 1011.104 1096.081 1083.542 1168.993 1084.859 1080.918 1167.957 1099.043 1094.379 1089.037 1165.233 1167.539 1032.183 1120.026 1121.875 1120.951 1046.585 1149.969 1144.009 1029.749 1117.821 1115.926 1040.571 1122.803 1120.503

-2.66 -1.50 -0.72 0.42 -1.73 -0.26 -5.37 -6.79 -2.46 -7.93 -3.24 -6.88 -1.71 -5.57 -9.51 -2.75 -3.90 -8.50 -2.72 -4.61 -2.31 -10.36 -2.80 -0.95 -1.88 -3.77 -11.93 -5.97 -11.58 -3.79 -1.90 -6.55 -4.60 -2.30

∆Gbind

K

λmax

-1.64

16b

355

665

-0.65

3b

312

395

-1.71

18b

473

620

-1.64

16

472

420

-2.79

112b

655

712

-2.09

34

485

537

-1.42

11

386

547

-1.36

10b

320

900

-1.68

17

418

581

a

Binding is described as π type if it is trulye an inclusion complex and σ type if it is centered about the cyclophane. Energies are reported in kcal/mol, association constants in M-1, λmax in nm, and in M-1 cm-1. b Data from Benniston, A. C.; Harriman, A.; Philp, D.; Stoddart, J. F. J. Am. Chem. Soc. 1993, 117, 5298. c The guest is symmetrically oriented in 14+. d The OH substituent is oriented toward the 14+ cavity. e The NH2 substituent is oriented toward the 14+ cavity. f The Cl substituent is oriented toward the 14+ cavity. g The averaged value of two conformations is compared with experiment. h The NO2 substituent is oriented toward the 14+ cavity. i The conformer with the guest oriented in the opposite direction to 14+ yields a binding energy close to zero. j The F substituent is oriented toward the 14+ cavity.

Energy Minimizations. The electrostatic potentials (ESP) of receptor 14+ and different guests were computed. In the case of 14+, the ESP was generated at a constant 250 kcal/mol, as shown in Figure 2. The resulting narrow cavity of receptor 14+ is ideally configured for aromatic systems. In fact, the interior cavity width and length from X-ray crystallography2 (6.8 × 10.3 Å) correspond to the dimensions found by theoretical considerations of stacked aromatic-aromatic interactions.31 The ESP for 5 was generated at -5 kcal/mol, and is a good representation of other 4,4′-substituted biphenyl derivatives, as shown in Figure 3. To begin the energy minimizations, the SPARTAN graphics interface was used to visually insert guests into the cavity of host 14+ on the basis of the qualitative representations given by combining the ESP plots of the host and guest. Several starting orientations were used to initiate the energy minimizations using PM3, AM1, and RHF/STO-3G calculations. Often, the AM1 method did not find stable inclusion complexes; instead the guest preferred to bind to the outside of 14+, forming a “lidlike” structure. The PM3 semiempirical method provided stable inclusion complexes for all of the systems considered. One complex of 3 plus 14+ was energy minimized using the RHF/STO-3G level of theory, as shown in Figure 4. The difference in the computed interaction energy is 1.4 kcal/mol. The PM3 method tends to give a slightly more symmetric binding complex than that produced by the RHF/STO-3G method. On the basis of the comparison of (31) Jorgensen, W. L.; Severance, D. L. J. Am. Chem. Soc. 1990, 112, 4768.

semiempirical methods with experimental and ab initio structural and energetic data, the PM3 method was selected for the remaining computations. Conformational Search. Since the 14+ host is tetracationic and the binding region has a narrow and well-defined cavity, the resulting complexes should be restricted to a limited conformational range. In order to probe the available conformational states for inclusion complexation, several random geometries were selected as the starting points for energy minimization for benzene plus 14+. For this particular system, energy minimizations using the PM3 Hamiltonian resulted in only three supramolecular complexes, as shown in Figure 5. The first computed complex has benzene centrosymmetrically located within the cyclophane cavity with a binding energy of -2.29 kcal/mol. The second complex has benzene symmetrically oriented in the pocket of the cyclophane, but slightly displaced (1-2 Å) along the axis of entry through 14+. The complexation energy of this configuration is more favorable at -5.35 kcal/mol. Finally, the third supramolecular complex is one where benzene is completely removed from the cavity region and strongly interacts (-8.62 kcal/mol) with the R and β protons on a paraquat group of 14+. Jorgensen et al. have reported that the gas-phase optimization of a “tilted T” benzene dimer structure has an interaction energy of -2.31 kcal/mol.31 This value is in excellent agreement with that reported from high-precision ionization measurements (-2.4 ( 0.4 kcal/mol).32 The “shifted-stacked” structure was computed to be -2.11 kcal/mol in energy. The PM3-computed


Castro et al.

Table 3. Computed Energies of Complexation between Monosubstituted Biphenyl Guests and 14+ a system


type

Hguest

Hcomplex

∆Hbind

0 12 0 12 0 12 0 12 0 12 12 0 12 0 12 12 0 0 0 12 0 12 12

π π σ σ π π σb σb σc σc avd σe σe σf σf avd πg πh σh σh σg σg avd

47.578

1111.003 1196.786 1108.152 1196.715 1062.734 1151.542 1061.227 1149.851 1063.030 1151.851 1150.851 1066.995 1156.268 1069.580 1158.573 1157.421 1106.008 1103.263 1100.983 1192.060 1106.138 1194.802 1193.431

-7.51 -2.01 -10.36 -2.08 -10.62 -2.09 -12.13 -3.78 -10.32 -1.78 -2.78 -13.54 -4.54 -10.95 -2.24 -3.39 -10.20 -12.95 -15.23 -4.43 -10.07 -1.69 -3.06

biphenyl

4-phenylphenol

4-phenylanisole

4-phenylaniline

2.415

9.592

45.272

∆Gbind

K

λmax

-2.30

49

442

457

-2.14

37

437

482

-2.90

133

525

545

a

Binding is described as π type if it is truly an inclusion complex and as σ type if it is centered about the cyclophane. Energies are reported in kcal/mol, association constants in M-1, λmax in nm, and in M-1 cm-1. b The OH substituent is oriented away from the 14+ cavity. c The OH substituent is oriented toward the 14+ cavity. d The averaged value of two conformations is compared with experiment. e The OMe substituent is oriented away from the 14+ cavity. f The OMe substituent is oriented toward the 14+ cavity. g The NH2 substituent is oriented toward the 14+ cavity. h The NH substituent is oriented away from the 14+ cavity. 2 Table 4. Computed Energies of Complexation between Disubstituted Biphenyl Guests with 14+ a system 4,4′-biphenol

benzidine

4,4′-dimethoxybiphenyl 4,4′-dimercaptobiphenyl 4,4′-diphosphinobiphenyl


type

0 12 0 12 0 12 12 0 12 0 12 0 0 0 0 0 0

πb πb πc πc σ σ avd πc πc πb πb π σ π σ π πb

Hguest -42.700

43.032

-28.350 55.948 58.629 43.032

Hcomplex

∆Hbind

1020.699 1105.902 1019.153 1114.703 1016.124 1103.478 1104.690 1099.581 1193.553 1099.060 1189.403 1031.235 1028.764 1120.467 1117.531 1123.695 1098.994

-7.54 -2.62 -9.08 -6.19 -12.11 -5.04 -3.83 -14.39 -0.70 -14.91 -4.85 -11.35 -13.82 -6.42 -9.35 -5.87 -14.98

∆Gbind

K

λmax

-2.93

140

500

438

-4.12

1044

644

557

a Binding is described as π type if it is truly an inclusion complex and as σ type if it is centered about the cyclophane. Energies are reported in kcal/mol, association constants in M-1, λmax in nm, and in M-1 cm-1. b The guest is planar. c The guest is twisted. d The averaged value of two conformations is compared with experiment.

14+/benzene complexes (Figure 5) have been analyzed using the structural and energetic data provided by Jorgensen. For the centrosymmetric complex, the benzene guest is centered within the 14+ cavity, resulting in two strong tilted T and four shifted-stacked interactions with the host. The two tilted T interactions should be roughly twice that reported by Jorgensen for the benzene dimer (-2.31 kcal/mol). The shifted-stacked interaction energies (-2.11 kcal/mol) can also be used to approximate the four benzene-paraquat interactions found in the 14+ complex. Thus, a total interaction energy of -13.06 kcal/mol, based upon Jorgensen’s work, can be used to estimate qualitatively the exclusion repulsive force (+10.75 kcal/mol) necessary to produce the predicted interaction energy of the 14+/ benzene complex (-2.31 kcal/mol). The origin of the second computed complex with benzene slightly outside the cyclophane (32) Grover, R.; Walters, E. A.; Hui, E. T. J. Phys. Chem. 1987, 91, 3233.

binding pocket (Figure 5) is a direct result of relieving the repulsive exclusion force from the cavity at the expense of losing the two tilted T structures to gain extra stability (-5.35 kcal/ mol). The third configuration is considered to be a gas-phase artifact, since no stationary point could be located when 12 acetonitriles were added. UV-Vis Binding Studies. Receptor 14+ is colorless in solution, until an aromatic guest is added. A charge-transfer band occurs if suitable intermolecular interactions develop between the guest and 14+, which provides a straightforward method to quantitate the free energy of complexation. The binding constants obtained from the UV-vis titrations of host 14+ with various guests show two major trends: (1) nitrogensubstituted aromatic molecules bind to 14+ with greater affinity than oxygen-substituted systems and (2) 4,4′-substituted biphenyl molecules bind to 14+ better than 1,4-substituted phenyl derivatives. Electron-withdrawing substituents decrease binding,



Figure 6. PM3-predicted enthalpic binding energies vs experimentally determined free energies of binding. The supramolecular model for the computations did not use any solvent.

as in p-chloroaniline, p-chlorophenol, p-aminobenzoic acid, and p-aminobenzoic acid methyl ester. Two donating para substituents enhance binding, except for hydroquinone and its bis(methyl ether), which are actually poorer binders than phenol and anisole. Replacement of a phenol with its methyl ether reduces the binding except for hydroquinone which seems to have the same value whether one or both of the phenols are methylated. Since both phenol and anisole similarly insert into the cavity of 14+, a steric effect could be in operation or the difference could be due to a favorable proton-aromatic ring type interaction which methylation eliminates. Methylation of the amines cannot be similarly rationalized since rotation of the dimethylamino group, and thus delocalization of its electron pair, is hindered with respect to the amino group, and monomethylation still leaves one amino hydrogen whereas the methylated phenol has none. Replacement of oxygen with sulfur lowers the binding constant contrary to the notion that a softer sulfur would be a better donor and therefore increase the binding. Unfortunately, this trend could not be examined further because thiophenol and other related compounds with a thiol or dimethylphosphino group reduce 14+ to its 3+ cation radical. Hence, only the corresponding methyl sulfides could be used. An interesting case is presented by p-aminophenol. While its binding constant is much larger than phenol’s, it is also larger than the binding constant for p-phenylenediamine. This is strange since nitrogen is a much better donor. Possibly, the asymmetry of the system could be a factor. Obviously, simple additive effects are not the general rule in these systems since combinations of the best donors do not always give the best binders. The biphenyl systems have less localized electron density than the phenyl systems, yet are better binders with 14+. Some other property must be governing the binding, a property of the system as a whole that takes into account not only the number and type of substituents but also how they interact with each other and with the ring system to which they are attached. Solvation. The gas-phase enthalpies of complexation have been computed using the PM3 method, as listed in Tables 1-4. The binding energies are determined by subtracting the energies computed for the isolated guest and the solvated host from the energy of the supramolecular system. The comparison between the experimental free energies and PM3-computed enthalpies is shown in Figure 6. A linear trend results, but the computed enthalpies of complexation are ca. 3 times greater than the free energies of complexation found by the UV-vis experiments. The computed absolute binding energies could be influenced

Figure 7. PM3-minimized complexes of 14+ with acetonitrile.

by the absence of counterions and solvent,33 incomplete description of the conformation distributions,34 level of theory used for evaluation,35 or a constant entropic term. Our curiosity concerning the overestimated binding energies was further enhanced by the fact that when either acetonitrile or water was placed into the center of the 14+ cavity, both solvents energy minimized to either the R or β protons on the paraquat units of 14+, as shown in Figure 7. PM3 yields -20.7 kcal/mol for the acetonitrile/14+ system at the β-protons and -23.3 kcal/mol at the R-proton. The β-proton complex forms a bifurcated system where the acetonitrile nitrogen is equally shared between the two protons. In order to test the unique strength of these interactions, a model system of methyl viologen plus acetonitrile was computed, as shown in Figure 8. The PM3, RHF/3-21G, and RHF/6-31G(D) methods yield -23.2, -27.8, and -23.4 kcal/mol for the R-interactions. In comparison, the β-interactions were computed to be -20.7, -22.5, and -18.5 kcal/mol, respectively. These results suggest that the protons are highly solvated and that the computed results will be improved by including solvent in these specific positions. The influence of solvent upon computed binding affinity was further investigated by systematically adding solvent molecules to 14+. First, two acetonitriles were added to the regions corresponding to the paraquat β-protons on one face of 14+. PM3 geometry optimizations resulted in a symmetric structure, as shown in Figure 7, for one acetonitrile. Two bifurcated hydrogen bonds result, with each acetonitrile sharing both bipyridinium β-protons from the paraquat units. Thus, a second pair of acetonitriles was subsequently added to the opposite face of the cyclophane for the shared β-protons, and (33) (a) Mirzoian, A.; Kaifer, A. E. J. Org. Chem. 1995, 60, 8093. (b) Denti, T. Z. M.; van Gunsteren, W. F.; Diederich, F. J. Am. Chem. Soc. 1996, 118, 6044. (34) Frauenfelder, H.; Wolynes, P. G. Phys. Today 1994, 58. (35) Ochterski, J. W.; Petersson, G. A.; Wiberg, K. B. J. Am. Chem. Soc. 1995, 117, 11299.


Castro et al. Table 5. PM3-Computed Effect of Acetonitrile on Binding Energies system

Hform

∆Hbind

∆Hbind/CH3CN

acetonitrile 14+ 14+ + 2MeCN 14+ + 4MeCN 14+ + 6MeCN 14+ + 12MeCN

23.285 1070.937 1077.346 1088.215 1095.045 1151.218

-40.2 -75.9 -115.6 -199.1

-20.1 -19.0 -19.3 -16.6

Figure 10. PM3-predicted enthalpic binding energies vs experimentally determined free energies of binding. The supramolecular model for the computations used 12 solvent molecules. Figure 8. 6-31G(D)-minimized complexes of methyl viologen with acetonitrile.

Figure 9. Supramolecular complex of 12 acetonitriles, benzene, and 14+.

one acetonitrile was added for every R-proton for a total of twelve acetonitriles per cyclophane, as shown in Figure 9. The computed energies for incremental addition of solvent molecules are given in Table 5. The energetic effect of acetonitrile addition on 14+ complexes is shown in Tables 1-4. The experimental free energy of binding between 14+ and benzene is -1.68 kcal/mol. The computed enthalpic energy of binding is -5.35 kcal/mol with no solvent and -4.03, -3.35, -3.06, and -1.67 kcal/mol for two, four, six, and twelve acetonitriles, respectively. In this particular case, the agreement between theory and experimental binding energies is within 0.01 kcal/mol, but in general, the

computed binding enthalpy is within 1 kcal/mol of the experimental free energy of binding. Each substituted phenyl and biphenyl system was recomputed in the presence of the 12 acetonitriles. In a few cases, more than one stable complex was located. In the event that multiple complexes were identified, the resulting energies of binding for each minimized conformation were averaged and then compared to experiment. The computed enthalpies of complexation, when compared to the experimental free energies, provide a linear correlation, as shown in Figure 10. Thus, the energetic consequences of the first solVation sphere of these complexes can be approximated by the 12 specific acetonitriles included in our computational model. Interestingly, no counterions were necessary to describe the structural and energetic behavior of 14+ complexes with substituted phenyl and biphenyl compounds. The structural behavior of 4,4′-substituted biphenyl guests emphasizes the importance of solvation in these particular hostguest systems.23-25 The planar transition structure (D2h) which separates the equivalent minima of biphenyl has low activation barriers for PM3, RHF/3-21G, and RHF/6-31G(D),23 consistent with the experimental value of 1.43 kcal/mol.36 For example, we compute that when benzidine initially inserts into 14+ that the large biphenyl twist prevents complete penetration into the cavity. The resulting complexation energy is -0.7 kcal/mol, but as the benzidine flattens and inserts deeper into the 14+ cavity the binding energy drops to -4.9 kcal/mol. The observed destabilization is caused by the twisted phenyl unit interfering with the strong electrostatic interaction between the bifurcated acetonitriles and the β-hydrogens on 14+. As shown in Figure 11, two acetonitriles are displaced 1 Å away from the region of maximum electrostatic interaction with the β-protons on 14+. The disrupted solvents are computed to regain their optimal positions around 14+ as benzidine inserts to provide a maximum solvation effect. The implication is that the supramolecular system gains additional stability from the solvent as the guest molecule passes through the center of 14+, since it must become (36) Bastiansen, O.; Samdal, S. J. Mol. Struct. 1985, 128, 115.


Figure 11. The twisted conformation of benzidine disrupts solvation. The acetonitriles (black) show the 1 Å movement away from the β-protons on 14+.

planar to thread through the center of the cyclophane. Thus, solVent is computed to be a major contributor to the driVing force of inclusion complexation and can possibly be a factor in the threading mechanism required for rotaxane formation. In addition to the solvent effect, the binding of 4 with 14+ should not occur in the same symmetric fashion as with 5, since the hydroxyl lone pair will necessarily tilt the biphenyl entry in order to maximize the electrostatic binding within the cavity of 14+. The energy of complexation should be stronger for 5 as compared to 4, since the benzidine amino substituents are stronger Lewis bases than the hydroxyls of biphenol. NMR NOE studies on the different inclusion complexes (4 and 5 plus 14+) were recently reported.6 Due to the geometry of the inclusion complex between 4 and 14+, an NOE was detected between the hydroxyl hydrogen of biphenol and the bipyridinium β-protons of 14+. No NOE could be detected between the amine hydrogens of benzidine and the bipyridinium β-protons of 14+. PM3 energy minimizations were carried out on both complexes using 12 acetonitriles, as shown in Figure 12 (solvent removed for clarity). In agreement with the qualitative predictions made above, there are major differences in the binding structures. The resulting PM3 14+/benzidine complex is centrosymmetric in the cavity of the cyclophane. Both phenyl rings penetrate into the cavity and become planar so that solvation of the β-protons on 14+ can be achieved. Therefore, the amine hydrogens are far removed from the β-protons involved in the NOE experiments. The closest distance between the two sets of protons is 4.37 Å. The computed complex structure for 14+/biphenol reflects the difference in the electrostatics between 4 and 5. In order to position the available lone pair of biphenol near the paraquat nitrogens, the biphenol enters the cavity in a diagonal fashion. Therefore, the depth of penetration is more shallow than found with 5. The result is that the hydroxyl hydrogen is oriented closer to the β-protons being irradiated in the NOE experiments. The closest computed distance is 4.08 Å, which is close enough to yield an NOE signal, as found by experiment.6 Variational Energy Decomposition of the Intermolecular Bond. The components of intermolecular complexation include a variety of well-known forces, and range from moderately


Figure 12. Two views of the PM3-minimized complexes of 14+ with 4,4′-biphenol and benzidine. The 12 acetonitriles were removed for clarity.

strong to weak interaction energies.37,38 The collective strength of intermolecular bonds often provides a significant driving force to yield unique supramolecular structures, energetics, and properties.1 Experimental results have indicated that van der Waals interactions, electrostatic interactions, and desolvation are significant factors in the processes of molecular recognition.38a In addition, there is increasing evidence that charge-transfer and electron donor-acceptor forces are negligible when compared to the effects of electrostatics upon molecular recognition.38a One goal of our study is to address the origin of intermolecular forces responsible for 14+ complexes, since the current literature invokes charge-transfer to rationalize 14+ binding.2,3a Different techniques have been reported which decompose the energetic contributions to the intermolecular bond energy in order to better understand phenomena such as hydrogen bonding,39 donor-acceptor (EDA) complexes,39,40 metal-ligand interactions,41 and clustering of alkali metal cations.42 The energy and charge distribution methods (ECDD) by Morokuma and Kitaura-Morokuma have proven to be powerful tools for the direct evaluation of molecular interactions.39,43 The ECDD method is based upon the removal of specified elements from the Hartree-Fock matrix which define the individual components of the interaction energy. The interaction energy is partitioned into electrostatic (ES), polarization (PL), repulsive exchange (EX), charge-transfer (CT), and residual (MIX) terms:

∆ESCF ) ∆EES + ∆EPL + ∆EEX + ∆ECT + ∆EMIX (1) Since the intermediate wave functions used to compute the ES and PL terms are not antisymmetrized, the ECDD method yields (37) (a) Morokuma, K.; Kitaura, K. In Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; John Wiley and Sons: Bath, England, 1980; Vol. 1. (b) Benniston, A. C.; Harriman, A.; Lynch, V. M. J. Am. Chem. Soc. 1995, 117, 5275. (38) (a) Hunter, C. A. Chem. Soc. ReV. 1994, 101. (b) Hunter, H. A.; Sanders, J. K. M. J. Am. Chem. Soc. 1990, 112, 5525. (c) Dahl, T. Acta Chem. Scand. 1994, 48, 95. (39) (a) Morokuma, K. Acc. Chem. Res. 1977, 10, 294. (b) Chen, W.; Gordon, M. S. J. Phys. Chem. 1996, 100, 14316. (40) (a) Umeyama, H.; Morokuma, K. J. Am. Chem. Soc. 1977, 99, 1316. (b) Sevin, A.; Giessner-Prettre, C. Tetrahedron 1994, 50, 5387. (41) Frey, R.; Davidson, E. R. J. Chem. Phys. 1989, 90, 5555. (42) Glendening, E. D. J. Am. Chem. Soc. 1996, 118, 2473. (43) (a) Morokuma, K. J. Chem. Phys. 1971, 55, 1236. (b) Kitaura, K.; Morokuma, K. Int. J. Quantum Chem. 1976, 10, 325.


Castro et al.

Table 6. Variational Energy Decomposition of 14+ with Various Guest Moleculesa ∆E

ES

PL

EX

CT

MIX

STO-3G//PM3 BSSE corrected

Hydroquinone (2) -3.9 -6.7 -1.2 -1.3

6.8 8.4

-3.2 -2.6

0.4 0.9

STO-3G//STO-3G BSSE corrected STO-3G//PM3 BSSE corrected

p-Phenylenediamine (3) -8.9 -11.6 -1.4 -1.3 -7.3 -10.1 -1.0 -4.2

6.6 8.9 6.7 8.6

-2.8 -2.2 -3.1 -2.5

0.2 0.7 0.3 0.8


4,4′-Biphenol (4) -7.7 -4.4 -6.8 -5.8

5.3 6.5

-2.2 -1.8

0.4 0.7


Benzidine (5) -12.0 -9.4 -7.0 -8.9

7.6 9.3

-3.7 -3.0

0.5 1.2

a

Energies are reported in kcal/mol.

components that can potentially violate the Pauli exclusion principle.42,44 Hence, critical examination of these terms is required since they are not upper bounds on the exact energy. Failure of the ECDD can potentially occur with extended basis sets and in unnatural and compressed fragment separations. Despite the claim of problems with the model wave functions, the ECDD method has proven to be successful when carefully monitored. The PM3 method yields structures which compare well with experiment and higher level theory for the complexes of interest. Typically, ab initio wave functions are used for the ECDD treatment of ab initio structures. The question which remains is whether the PM3-generated structures are appropriate for an ab initio ECDD analysis. Thus, ECDD was carried out on the PM3-minimized water dimer geometry using the STO-3G, 3-21G, 6-31G(D), and 6-31G(P,D) basis sets. The energetic components from the ECDD method on the PM3-minimized geometries were computed to be within 0.2 kcal/mol of the energies from the corresponding ab initio structures. To delineate the forces which cause the computed binding enthalpies in our study, four molecular complexes, 2-5 plus 14+, were subjected to the ECDD method (Table 6). The minimized PM3 geometries of the complexes were used. The largest basis set affordable for ECDD with molecular complexes of 98 atoms was the STO-3G basis set. Each integral file used in the energy evaluation grew to be 1.9 Gbyte. The current maximum size of any UNIX file on modern computer workstations is 2 Gbyte. We are currently implementing direct SCF procedures to alleviate this current limitation. Our first observation is that basis set superposition error (BSSE) of the computed complexes was not as great as found with the water dimer.43 The proportion of BSSE correction to the total computed interaction energy ranged from 25 to 67% for the 2-5 plus 14+ complexes. The computed interaction energy from both PM3 and STO-3G is greater for 3 as compared to 2, and for 5 with respect to 4. The ECDD decomposition yields interesting insights into the processes and energies of inclusion complexation. First, the electrostatic contribution for both the substituted phenyl and biphenyl complexes with 14+ is expected to be underestimated as previously computed for the water dimer using the STO-3G basis set.43 Surprisingly, the electrostatic term is computed to dominate the energetic interactions between 14+ and either 2 or 3. For both the phenyl and biphenyl systems, the electrostatic contribution is approximately twice as large for the nitrogensubstituted guests as that found with their oxygen counterparts (44) Glendening, E. D.; Streitwieser, A. J. Chem. Phys. 1994, 100, 2900.

(compare 2 with 3 and 4 with 5). The repulsion-exchange term almost completely cancels the electrostatic stabilization provided by oxygen-substituted guests, yet only partially cancels the electrostatic stabilization from nitrogen-substituted systems. The charge-transfer contribution is relatively constant in the range between 2 and 3 kcal/mol for complexes 2-5 with 14+. Therefore, the charge-transfer stabilization does not reflect the experimentally determined differences in binding energies, as traditionally believed.2,3a The ECDD computations show that the stability of 14+ complexes is greater for the biphenyl systems 4 and 5 as compared to the analogous phenyl guests 2 and 3. The largest computed differential effect was seen in the polarizability of the complexes. We compute that the stabilization provided by polarizability increases from 1 to 7 kcal/mol when phenyl is replaced with biphenyl in the molecular systems studied. The delocalization resulting from extending the π-system of the guest significantly enhances the polarizability of the entire supramolecular complex. Thus, for all of the energetic components examined, the change in polarizability (not charge-transfer) is determined to be responsible for the differential binding effects that haVe been theoretically and experimentally obserVed. Molecular Polarizability. It is now common practice to compute molecular electrical moments and polarizabilities.45 Such computations have recently provided an advanced understanding of molecular properties and reactivity in chemical systems.46 The molecular properties of interest are defined as derivatives of an energy. For example, the dipole moment is formulated as the first derivative of the energy with respect to the strength of an applied field. The second derivative is defined to be the polarizability. The influence of basis set quality upon computed electrical properties has recently been examined in detail.46 The main result of the energy decomposition study is that the change in polarizability of the 14+ complex is determined to be responsible for the differential binding effects in 1,4substituted phenyl and 4,4′-substituted biphenyl derivatives. Due to well-documented problems with ECDD,44 we decided to explore the possibility that individual molecular properties of the guests would correlate with the computed binding energies with 14+. Such a correlation would support the ECDD studies. The 3-21G and 6-31G(D) basis sets were used to compute the electrical moments and polarizabilities of each isolated guest using restricted Hartree-Fock theory. The computed polarizability component along the principal molecular (biphenyl) axis is reported in Table 7. The polarizability values were compared with the associated enthalpies of binding and observed free energies of binding with 14+. The 3-21G polarizability along the principal molecular axis is a few percent lower than that computed using the 6-31G(D) basis set. A linear correlation between the computed polarizability for each guest and the enthalpy of binding of the 14+ complex (12 acetonitriles) results, as shown in Figure 13. The interpretation formulated is that a more polarizable molecule can electronically adapt to the unusual binding cavity of 14+, and this results in stronger binding energies. Benzidine yields the strongest observed and computed association constant for the series of 1,4-substituted phenyl and 4,4′-substituted biphenyl molecules tested. In addition, benzidine has the largest molecular polarizability component along the main axis of the biphenyl unit. Our intention was to use a (45) Dykstra, C. E.; Liu, S-H.; Malik, D. J. AdV. Chem. Phys. 1989, 75, 37. (46) (a) Toto, J. L.; Toto, T. T.; de Melo, C. P. J. Chem. Phys. 1995, 102, 8048. (b) Bursi, R.; Lankhorst, M.; Feil, D. J. Comput. Chem. 1995, 16, 545.



Table 7. Computed Polarizabilities (Å3) Using the RHF/3-21G and RHF/6-31G(D) Levels of Theorya molecule

E(6-31G*)

R3-21G R6-31G* ∆Hbind ∆Gbind

benzene -230.70314 64.9 toluene -269.74016 81.3 phenol -305.55768 71.4 anisole -344.58171 87.7 aniline -285.73070 79.9 tert-butylbenzene -386.83767 116.8 thiophenol -628.21031 94.7 thioanisole -668.24501 124.0 p-xylene -308.77700 98.8 1,4-dichlorobenzene -1148.50183 115.9 hydroquinone -380.40887 77.5 1,4-dimethoxybenzene -458.45783 110.9 1,4-phenylenediamine -340.75424 93.2 p-chloroaniline -744.63086 106.0 p-chlorophenol -764.45704 84.7 p-methoxytoluene -383.61802 88.6 biphenyl -460.25385 159.5 4-phenylphenol -535.10868 169.0 4-phenylanisole -574.13400 189.2 4-phenylaniline -515.28159 181.7 4,4′-biphenol -609.96327 177.7 benzidine -570.30344 200.6 4,4′-diphosphinobiphenyl -913.28249 275.1 water -76.01075 3.6 ammonia -56.18436 3.6 acetonitrile -131.92753 29.5

68.1 85.3 74.8 90.9 82.9 122.2 98.3 129.2 103.6 116.9 80.8 114.1 96.9 107.8 98.6 109.2 169.5 179.1 199.3 191.0 187.8 213.5 145.1 4.8 5.3 31.8

-1.67 -2.14 -3.01 -2.35 -2.33 -3.14 -2.44 -3.49 -1.50 -1.73 -2.46 -3.24 -2.75 -0.40 -1.88 -2.30 -2.08 -2.78 -3.39 -3.06 -3.83 -4.85 n/a n/a n/a n/a

-1.68 -1.64 -2.14 -1.74 -2.64 -0.95 n/a -1.71 -1.64 -0.65 -1.71 -1.64 -2.79 -2.09 -1.42 -1.68 n/a -2.30 -2.14 -2.90 -2.93 -4.12 n/a n/a n/a n/a

Figure 14. Comparison of the 6-31G(D)-computed binding energies and the molecular hardness of the guests.

a molecule can be regarded as its capacity to accept electronic charge. Formally, the hardness (η) and the electronic chemical potential (µ) are defined as the derivative of the energy (E) for a given number of electrons (N), potential due to nuclei (ν), and any other external potential. In practice, eqs 2 and 3 are

2η ) (∂2E/∂N2)ν,T ) (∂µ/∂N)ν,T

(2)

µ ) (∂E/∂N)ν,T

(3)

a

The computed enthalpy of complexation, ∆Hbind, and experimental free energy of binding, ∆Gbind, between 14+ and each guest is given in kcal/mol. All guests have been verified as ground state minima by frequency analysis.

Figure 13. Comparison of the 6-31G(D)-computed binding energies and the molecular polarizability of the guests.

more polarizable molecule, such as 4,4′-diphosphinobiphenyl, with the expectation that it would bind better with 14+. Unfortunately, we could not determine the experimental binding constant of 4,4′-diphosphinobiphenyl with 14+ due to the reduction of 14+. In addition, the predicted energies of complexation for both 4,4′-diphosphinobiphenyl and 4,4′dimercaptobiphenyl are actually smaller than found with the benzidine/14+ system, as shown in Table 4. The results indicate that a meaningful response in the binding energy occurs only between 60 and 200 Å3, where benzidine defines the upper limit. Polarizabilities outside of this region have only a constant effect on the binding energies. Therefore, for the first time, we haVe shown a direct correlation between computed molecular polarizability of the guest, within a certain window of polarizabilities, and the stability of the resulting 14+ complex. Principle of Maximum Hardness. It has been recently pointed out that the maximum hardness of an organic molecule can provide an intuitive understanding into its chemical behavior and reactivity.47,48 In hardness-softness terms, the softness of

replaced by a finite difference approximation which relates the chemical hardness (η) and chemical potential (µ) to the ionization potential and electron affinity. By invoking Koopman’s theorem, the orbital energies of the highest occupied (HOMO) and lowest unoccupied (LUMO) orbitals can be used to approximate both equations:

η ) (LUMO - HOMO)/2

(4)

µ ) (LUMO + HOMO)/2

(5)

The softness has been defined as the reciprocal of the hardness. Previous correlations among the hardness, polarizability, and size of atoms, molecules, and clusters have been demonstrated.48c The maximum hardness of a molecule has also been shown to be an excellent measure of aromaticity.48 In addition, the principle of maximum hardness in a chemical system is a measure of its resistance to changes in electronic configuration. Other novel relationships between the cube root of the polarizability and the dipole moment for both positively and negatively charged ions have been reported.48d In an effort to better understand the electronic nature of 14+, the orbital energy levels and electron affinities have been computed. The HOMO and SHOMO are doubly degenerate and stay closely spaced at all the levels of theory considered. This is consistent with the experimentally known two consecutive electron reduction potentials of 14+ to 12+ and 1.3a Previous use of Koopman’s theorem has shown that Hartree-Fock calculations with the minimal basis set are particularly inadequate for predicting electron affinities in other supramolecular systems, yet semiempirical methods when used with Koopman’s theorem have been shown to provide surprisingly accurate (47) Yang, W.; Parr, R. G. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 6723. (48) (a) Chattaraj, P. K.; Cedillo, A.; Parr, R. G.; Arnett, E. M. J. Org. Chem. 1995, 60, 4707. (b) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (c) Ghanty, T. K.; Ghosh, S. K. J. Phys. Chem. 1993, 97, 4951. (d) Pal, S.; Chandra, A. K. J. Phys. Chem. 1995, 99, 13865. (e) Makov, G. J. Phys. Chem. 1995, 99, 9337.


Castro et al.

Table 8. Computed RHF/6-31G(D) Orbital Energies of Mono- and 1,4-Disubstituted Phenyl and Biphenyl Guestsa system

E(6-31G(D))

EHOMO

ELUMO

hardness

softness

EN

benzene toluene chlorobenzene phenol anisole aniline tert-butylbenzene thiophenol phenylphosphine p-xylene 1,4-dichlorobenzene hydroquinone 1,4-dimethoxybenzene p-phenylenediamine 1,4-dimercaptobenzene 1,4-diphosphinobenzene p-fluorotoluene p-mercaptophenol p-methoxytoluene biphenyl 4-phenylphenol 4-phenylaniline 4,4′-biphenol benzidine 4,4′-diphosphinobiphenyl

-230.70314 -269.74015 -689.60335 -305.55768 -344.58171 -285.73070 -386.83767 -628.20892 -571.99284 -308.77696 -1148.50183 -380.40887 -458.45783 -340.75424 -1025.71376 -913.28249 -368.59127 -703.06217 -383.61802 -460.25385 -535.10868 -515.28159 -609.96327 -570.30344 -913.28249

-0.331 -0.319 -0.335 -0.309 -0.305 -0.289 -0.319 -0.306 -0.314 -0.308 -0.338 -0.292 -0.285 -0.262 -0.293 -0.304 -0.332 -0.292 -0.296 -0.300 -0.282 -0.274 -0.279 -0.258 -0.304

0.150 0.148 0.132 0.144 0.147 0.151 0.149 0.319 0.132 0.146 0.116 0.135 0.142 0.147 0.128 0.119 0.134 0.132 0.146 0.117 0.124 0.128 0.133 0.141 0.119

0.240 0.234 0.234 0.227 0.226 0.220 0.234 0.223 0.223 0.227 0.227 0.214 0.214 0.205 0.211 0.212 0.233 0.212 0.221 0.209 0.203 0.201 0.206 0.200 0.212

4.16 4.28 4.28 4.42 4.42 4.55 4.27 4.49 4.48 4.41 4.41 4.68 4.68 4.89 4.75 4.73 4.29 4.72 4.52 4.80 4.93 4.98 4.85 5.01 4.73

-0.091 -0.086 -0.102 -0.083 -0.079 -0.069 -0.085 -0.084 -0.091 -0.162 -0.111 -0.079 -0.072 -0.058 -0.083 -0.093 -0.099 -0.080 -0.075 -0.092 -0.079 -0.073 -0.073 -0.059 -0.093

a HF energies are reported in kcal/mol, and orbital energies are in eV. The absolute hardness is defined as (E LUMO - EHOMO)/2, the softness as the reciprocal, and the electronegativity as (ELUMO + EHOMO)/2.

electron affinities.49 In our specific system, the energy between the degenerate HOMO and degenerate virtual orbitals is between 0.25 and 0.26 eV for MNDO, PM3, and AM1. The HartreeFock-predicted differences are higher at 0.35, 0.34, and 0.33 eV using the STO-3G, 3-21G, and 6-31G(D) basis sets. Electronic structure calculations were carried out for over 20 substituted phenyl and biphenyl guests, as listed in Table 8. The correlation between molecular hardness and the computed 14+ binding affinities is shown in Figure 14, which is not as good as found with the molecular polarizability. The computed trend between molecular hardness of the individual guest molecules and the binding energies of 14+ complexes is consistent with the idea that guests which resist changes in their electronic configuration also result in low binding energies with 14+. Conclusions The energy components of the intermolecular bond have been evaluated in inclusion complexes involving the tetracationic cyclophane receptor 14+ and 1,4-substituted phenyl and 4,4′substituted biphenyl guests. Excellent agreement between observed and predicted structures and binding affinities have been found. The role of solvent has been addressed, and a first solvation shell of 12 acetonitriles has been shown to account for many of the observed structural and energetic properties of the 14+ complexes. We have shown by using semiempirical and ab initio molecular orbital theory that the basis of molecular recognition is governed by cavity binding composed of strong electrostatic and small charge-transfer forces for 1,4-substituted (49) Cioslowski, J. Electronic Structure Calculations on Fullerenes and Their DeriVatiVes; Oxford University Press: New York, 1995; Chapter 3.

phenyl systems. The largest intermolecular differential force driving the inclusion complexation in 1,4-substituted phenyl and 4,4′-substituted biphenyl guests is polarizability. For the first time, we have shown a direct correlation between computed molecular properties of the guest and the strength of the resulting 14+ complex. The molecular polarizability and maximum hardness of the guest can be used as predictive tools in the design of new and useful molecular devices. Two main chemical factors which rationalize the differential binding have been identified and linked to the (1) Lewis basicity of nitrogenvs oxygen-containing substituents and (2) delocalization of biphenyl vs phenyl units of the guest molecule. While 14+ is a unique receptor, the methods and conclusions presented here to understand the structure and energetics of the intermolecular bond are applicable to more generalized situations in supramolecular chemistry. Acknowledgment. We are grateful to the Maytag doctoral fellowship from the University of Miami (to M.J.B.), Gobierno de Navarra (to M.O.d.O.), the National Science Foundation (to A.E.K., Grants CHE-9304262 and CHE-9633434), the Summer Award in Natural Science and Engineering and the University of Research Council from the University of Miami (to J.D.E.), the Petroleum Research Fund (to J.D.E., Grant PRF#30918G4), and the Department of Defense (to J.D.E., Grant DAAH0496-1-0311) for financial support of this research. Supporting Information Available: Semiempirical and ab initio energies, structures, and frequencies in either GAUSSIAN or SPARTAN archive format (163 pages). See any current masthead page for ordering and Internet access instructions. JA960700X

Unexpected Roles of Guest Polarizability and Maximum Hardness

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